Silver soldering should provide the strength you
need, I'm not sure of conductivity.

Parron,
 
You can weld copper.  I had a project a few years back that required welding 0.5 inch (12.5mm) thick copper and 0.25 inch copper plate together on a process vessel.  After 10 years of service there are no problems with the work that was done.  

On your component, there should be not be a problem with electrical conductivity and the tensile strength would be very close if not the same to the base material.  

Most people don't know how to do it or where to go to get it done.  If you want additional help contact me.

Motor manufactures weld copper all the time where electrical and mechanical joint integrity is important. The connectors are insulated so heat must be kept low so a TIG welding process is used. Since the weld penetration will only be say 30 mills deep, electrical contact is enhanced by placing a piece of silver alloy (pre-place foil) between the surfaces before welding; the welding heat melts the alloy at the same time. I think this process is called TIG brazing (?).

Parron,
Depending upon your application and requirements you may want full penitration welds for strength.  
ENC

To provide conductivity we offer to customers ultrasonic welding machine which uses molocular bonding system.
We sell this machine to solar energy comapnies for welding copper fins to copper tubes without loosing conductivity.
for more information our mail address: intersun@siberg.com